www.bbc.co.uk/news/uk-england-birmingham-30251741
I think its already quite easy for a decent landlord to avoid illegal immigrants by using a referencing company. Its not in a landlord's interest to have a tenant deported and unable to pay the rent. I don't see why further measures are needed.
I am concerned that legal immigrants will find it impossible to find rental accomodiation. It will be simpler for a landlord just to pick the white applicant who has a british passport. It will end up being the 1960s where adverts said "no blacks - no irish".